I may be totally wrong here but I think perhaps the distinction between Access, which provides both the storage engine and the interface, and Mysql, which only provides the storage engine, may be tripping you up.
Mysql, by itself, is just a storage engine without any human-friendly interface. It accepts SQL commands to select, insert, update, or delete your data. It can do sorting and searching and that kind of stuff. But the friendly interface parts are not included as they are in Access.
At dreamhost, you can use phpMyAdmin, a reasonably friendly “administrator view” interface to the database. When you set up the mysql database, you assign it a hostname. Enter that hostname in a browser, log in to the resulting prompt with the database username and password you set up in the control panel, and you are administering your database via phpMyAdmin. This would be good for transferring your data from Access, making administrative updates, downloading a backup, etc.
For your website users, it’s probably not a good idea to allow them access to the database via phpMyAdmin. It’s not that friendly an interface for the general public, and you would not have enough access control to prevent vandalism of your database. For public web purposes, you would have to build a web site in one of the scripting languages dreamhost supports (perl, php, ruby, etc.) that can issue the SQL commands to read, search, and update your mysql database (in an appropriately access-limited way).
I’m sorry if that was too basic or totally off-topic; hope it helps.